Magnetocrystalline anisotropy energy of Fe(001)(001), Fe(110)(110) slabs and nanoclusters: a detailed local analysis within a tight-binding model

We report tight-binding (TB) calculations of magnetocrystalline anisotropy energy (MAE) of Iron slabs and nanoclusters with a particuler focus on local analysis. After clarifying various concepts and formulations for the determination of MAE, we apply our realistic TB model to the analysis of the magnetic anisotropy of Fe$(001)$, Fe$(110)$ slabs and of two large Fe clusters with $(001)$ and $(110)$ facets only: a truncated pyramid and a truncated bipyramid containg 620 and 1096 atoms, respectively. It is shown that the MAE of slabs originates mainly from outer layers, a small contribution from the bulk gives rise, however, to an oscillatory behavior for large thicknesses. Interestingly, the MAE of the nanoclusters considered is almost solely due to $(001)$ facets and the base perimeter of the pyramid. We believe that this fact could be used to efficiently control the anisotropy of Iron nanoparticles and could also have consequences on their spin dynamics

Two-photon absorption in two-dimensional materials: The case of hexagonal boron nitride

13 pages, 4 figuresInternational audienceWe calculate the two-photon absorption in bulk and single layer hexagonal boron nitride (hBN) both by an ab-initio real-time Bethe-Salpeter approach and by a the real-space solution of the excitonic problem in tight-binding formalism. The two-photon absorption obeys different selection rules from those governing linear optics and therefore provides complementary information on the electronic excitations of hBN. Combining the results from the simulations with a symmetry analysis we show that two-photon absorption is able to probe the lowest energy $1s$ states in the single layer hBN and the lowest dark degenerate dark states of bulk hBN. This deviation from the "usual" selection rules based on the continuous hydrogenic model is explained within a simple model that accounts for the crystalline symmetry. The same model can be applied to other two-dimensional materials with the same point-group symmetry, such as the transition metal chalcogenides. We also discuss the selection rules related to the inversion symmetry of the bulk layer stacking

Excitons in few-layer hexagonal boron nitride: Davydov splitting and surface localization

Hexagonal boron nitride (hBN) has been attracting great attention because of its strong excitonic effects. Taking into account few-layer systems, we investigate theoretically the effects of the number of layers on quasiparticle energies, absorption spectra, and excitonic states, placing particular focus on the Davydov splitting of the lowest bound excitons. We describe how the inter-layer interaction as well as the variation in electronic screening as a function of layer number N affects the electronic and optical properties. Using both ab initio calculations and a tight-binding model for an effective Hamiltonian describing the excitons, we characterize in detail the symmetry of the excitonic wavefunctions and the selection rules for their coupling to incoming light. We show that for N > 2, one can distinguish between surface excitons that are mostly localized on the outer layers and inner excitons, leading to an asymmetry in the energy separation between split excitonic states. In particular, the bound surface excitons lie lower in energy than their inner counterparts. Additionally, this enables us to show how the layer thickness affects the shape of the absorption spectrum

Giant tunnel-electron injection in nitrogen-doped graphene

International audienceScanning tunneling microscopy experiments have been performed to measure the local electron injection in nitrogen-doped graphene on SiC(000¯1) and were successfully compared to ab initio calculations. In graphene, a gaplike feature is measured around the Fermi level due to a phonon-mediated tunneling channel. At nitrogen sites, this feature vanishes due to an increase of the elastic channel that is allowed because of symmetry breaking induced by the nitrogen atoms. A large conductance enhancement by a factor of up to 500 was measured at the Fermi level by comparing local spectroscopy at nitrogen sites and at carbon sites. Nitrogen doping can therefore be proposed as a way to improve tunnel-electron injection in graphene

Momentum resolved spectroscopy of the dielectric response by TEM

International audienceConsidering dielectric properties of 2D materials, specific questions arise among the screening effects of charge carriers or effects induced by the substrate and highlight the necessity of studying these properties on free standing pristine layers. This can be done using electron energy loss spectroscopy in the low loss energy range (Low-EELS) related to interband and plasmons excitations. Furthermore, in contrast to standard optical spectroscopies, the transfer momentum dependence of the excitations is accessible from the measured loss function provided to operate an angular resolved EELS. Measuring the q dependence of the loss function needs to build a data cube in the diffraction space relying energy losses and q vectors in the diffraction plane. In this work, this is operated employing an electron energy spectroscopic set up in a Libra 200 TEM equipped with an electrostatic monochromator operated in the 40-80 kV range, an in-column corrected omega filter and a CCD camera thanks to which a spectral resolution below 100 meV can be achieved at 40 kV. This set-up provides high quality energy-loss spectra in the form of ω-q maps obtained by selecting a q direction thanks to a slit implemented at the entrance of the omega filter and allows also for the imaging of energy-filtered diffraction patterns. These two acquisition modes provide complementary pieces of information, offering a global view of excitations in reciprocal space. We present here the capabilities of this setup through the study of various 2D layered materials. The Figure 1 displays low losses spectra of pristine mechanically exfoliated phosphorene flakes showing a clear energy upshift of the excitation onset upon thickness decreasing. Optical gaps deduced from these spectra indicate values varying from 1 eV to 1.9 eV between the 3L and the monolayer, which are very close to theoretical predictions. In the same way a blue shift from 1.4 to 1.8 eV of the optical gap has been measured in MoS2 between multilayers and the monolayer.Figures 2 and 3 summarize measures of the low losses associated with interband and /or plasmon excitations performed on hexagonal boron nitride single crystals cut along different directions of the Brillouin zone. First, energy filtered patterns in the basal plane reveal the symmetries of the dipole matrix elements involved in the observed transitions and reveal the direct and indirect nature of the excitations observed for the low losses at 8 and 12 eV respectively. Moreover, by comparing these patterns with our specific ab initio calculations, we show that we are able to relate the range of applicability of ab initio calculations to the anisotropy of the sample and assess the level of approximation required for a proper simulation. Second, intensity profiles extracted from ω-q maps recorded along different directions of the Brillouin zone allow to illustrate that our method provides results which quality is comparable to that obtained from non resonant x-ray inelastic scattering but with advantageous specificities such as an enhanced sensitivity at low q and a much greater simplicity and versatility that make it well adapted to the study of two-dimensional materials and related heterostructures

Variational and mean field formulations of the cluster variation method and of the path probability method

To be published in : Progress Theoretical PhysicsSIGLEAvailable at INIST (FR), Document Supply Service, under shelf-number : 22419, issue : a.1993 n.11 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc